Waves in Pipes and String - 15+ Short Questions With Answer | Physics Class 12

Short Question Answer | Physics
Short Questions-Answer from Waves in Pipes and Strings
Class: 12

1)The frequency of fundamental note of an open organ pipe is double than for closed pipe of same length .Why?

When an air column in an organ pipe is set into vibration, the air column must vibrate with an anti node in case of open organ pipe and a node in case of closed organ pipe. The ends of open organ pipe are antinodes and middle point is node in the fundamental note. If l be the length of pipe and λ0 be the wavelength, then  l =λ0/2 or λ0=2l

So frequency of fundamental note f0 =v/λ1 =v/2l …………..(i)

While in closed organ pipe, the closed end is node and open end is antinode. If l be the length of pipe and λc be the wavelength, then 

l =λc/4 of λc = 4l

So, frequency of fundamental note is given by 

Fc= v/λ =v/4l ………..(ii)

Therefore, from (i) and (ii) f0 =2fc

That is, the frequency of fundamental note of an open organ pipe is double than for closed pipe of same length.

2) The frequency of organ pipe changes with temperature. Does it increase with increase in temperature?

As we know that the frequency of an organ pipe is directly proportional to the velocity of sound in air i.e. f v.

We have,  V= (yp/p)^(1/2)

Where P is pressure, ρ is density and γ is the ratio of two heat capacities.

We have, PV =RT for one mole of ideal gas

Or, PM/ρ =RT ………….(ii) Since M=V×ρ

From (i) and (ii), we have 

V = (yRT/M)^(1/2)

V= (yR/M)^(1/2)  × (T)^(1/2)

V= K(T)^(1/2)                       where K= yR/M)^(1/2)  is a constant

α

So, v α v and so f α (T)^(1/2) , This shows that frequency of an organ pipe is directly proportional to the square root of the absolute temperature. Thus, if the temperature of the organ pipe is increased, its frequency will be also increased.

3) Explain why soldiers are ordered to break steps while crossing a bridge.

Soldiers are ordered to break steps while crossing bridge. If the marching soldiers do not break the steps, the frequency of marching may exactly coincide with the natural frequency of the bridge and the resonance occurs in the bridge, and it vibrates with maximum amplitude. If the displacement of the bridge exceeds the elastic limit of the bridge, it may collapse. So soldiers are ordered to break steps while crossing bridge.

4) Why is and end correction necessary for an organ pipe?

When an air in an organ pipe vibrates, the reflection of the sound waves takes place a little above the open end of the pipe. So the length of the air column which has been set into oscillation is not exactly the distance between the two ends of the tube but a little bit more than this. This factor is to be considered in order to get the accurate value for frequency of vibration. So, the end correction is necessary for an organ pipe.

5) Relate the fundamental note with overtone for an open pipe.

Frequency of the lowest note obtainable from pipe is called its fundamental note. For an open pipe, it is f0 = v/ 2l where v is speed of waves and l is length of the pipe. The frequencies of the overtones in open pipe are the integer multiple of f0. That is, the frequencies of overtones are 2f0, 3f0, 4f0 and so on.

6) Why is sonometer box hollow from inside?

When the stem of vibrating tuning fork is gently passed against the top face of sonometer box, the air enclosed in the box will vibrate. This increases the intensity of sound. The hole in the side of the sonometer box bring the inside air in contact with the outside air and hence check the effect of elastic fatigue.

7) What do you mean by resonance? 

When a system is made to execute forced vibration by applying a periodic force of the same frequency as the natural frequency of the system, it is said to execute resonance. If the external periodic force is always in phase with the natural frequency of the system, amplitude progressively builds up and it soon becomes very large. When the frequency of the source is equal to the natural frequency of the body, the body begins to vibrate with maximum amplitude and this kind of vibration of the body is known as resonant vibration.

8) One of the “ Nine Jewels” of Emperor Akbar, widely known as Tansen, the king of music, was able to break a glass by singing the appropriate note. What physical phenomenon could account for this?

The frequency of the sound coming from Tansen singing may match with the natural frequency of the glass, and resonance may occur. In this case, even small sound coming from the source may cause the glass molecules to vibrate with amplitudes exceeding their elastic limit and cause breaking. In this way, Tansen, the king of music was able to break glass by singing the appropriate note.

9) Why is the loud heard at resonance?

At resonance, natural frequency of a body is equal to the frequency of externally applied periodic source. From the principle of superposition, the intensity and hence amplitude of resulting wave is maximum. So, loud sound is heard in this condition. This is because loudness depends on intensity of sound.

10) Why are rubbers used as vibration absorber?

Rubbers are used as vibration absorbers because, in their unstretched state, their molecules are coiled and can be stretched. Thus, during compressing and stretching, a large potential energy can be stored and it elapes slowly. During vibration, it can store vibrational kinetic energy and releases slowly. Due to this, they possess elastic histerasis. So rubbers are used as vibration absorbers.

11) When the tension in a given stretched string is increased by four times, by what factor does the velocity of transverse wave in the string change?

The velocity of the transverse wave propagating through the string is given by v= (T/m)^(1/2), where T is the tension in the string and m is the mass per unit length of the string. When the tension in the string is increased by four times, then the velocity of the wave in the string becomes,

V1= (4T/m)^(1/2)  =2 (T/m)^(1/2)  =2v

i.e. The velocity of transverse wave in the string becomes double.

12) Is the wave speed the same as the speed of any part of the string for transverse waves? Explain the difference between these two speeds.

The speed of a vibrating particle of the medium is different at its different positions in a vibration but the speed of the wave motion is always constant. In other words, the particle speed varies with time, while the wave speed is independent of time.

13) If the frequency of a fundamental note of a closed pipe and that of an open pipe are the same, what will be the ratio between these two speeds?

Let lc and lo be the lengths of a closed and open pipes respectively and v be the velocity of sound in air

Frequency of a fundamental note of a close pipe, fc= v/4lc and that of an open pipe,

Fo=v/2lo

Now, according to the question,

fc=fo

or, v/4lc=v/2lo

therefore, lc/lo =1/2

14) Is it possible to have a longitudinal wave on a stretched string? Why or Why not?

It is possible to have a longitudinal wave on a stretched string by stroking it along its length by a rosined cloth. However, in the wave motion of a stretched string ( tant string with fixed ends) wave (disturbance) produced at one fixed end travels along the length of the string and get reflected back at the other end. Since the original wave and the reflected wave have the same frequency and amplitude, they superimpose to produce stationary transverse wave.

15) What happens to the frequency of transverse vibration of a stretched string if its tension is halved and the area of cross section of the string is doubled?

The frequency of transverse vibration of a stretched string is given by 

F= (1/2l) × (T/m)^(1/2) , where T is the tension in the string and m is the mass per unit length of the string  (=A×ρ)

When the tension in the string is halved and the area of cross-section is doubled, then the frequency becomes

F1= (1/2l) × (T/2×2m)^(1/2)  = 1/2 ×(1/2l) × (T/2×2m)^(1/2)        =1/2 (f)

i.e. the frequency of transverse vibration of a stretched string becomes half of its initial value.

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