A uniform rope of length \(L\) and mass \(m_1\) hangs vertically from a rigid support. A block of mass \(m_2\) is attached to the free end of the ropes. A transverse pulse of wavelength \(\lambda_1\) is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is \(\lambda_2\). The ratio \(\dfrac{\lambda_2}{\lambda_1}\) is:
1. \(\sqrt{\dfrac{m_1+m_2}{m_1}}\)
2. \(\sqrt{\dfrac{m_2}{m_1}}\)
3. \(\sqrt{\dfrac{m_1+m_2}{m_2}}\)
4. \(\sqrt{\dfrac{m_1}{m_2}}\)

A source of sound S emitting waves of frequency 100 Hz and an observer O are located at some distance from each other. The source is moving with a speed of 19.4 ms^-1 at an angle of 60° with the source observer line as shown in the figure. The observer is at rest. The apparent frequency observed by the observer (velocity of sound to air 330 ms^-1), is

1. 100 Hz
 

2. 103Hz
 

3. 106 Hz
 

4. 97 Hz

4.0 g of a gas occupies 22.4 L at NTP. The specific heat capacity of the gas at constant volume is 5.0 J K^-1mol^-1. If the speed of sound in this gas at NTP is$952 m{s}^{-1}$, then the heat capacity at constant pressure is: (Take gas constant R=8.3 JK^-1mol^-1)

1. 8.0 JK^-1mol^-1
 

2. 7.5 JK^-1mol^-1
 

3. 7.0 JK^-1mol^-1
 

4. 8.5 JK^-1mol^-1

If n₁, n₂ and n₃ are, are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency n of the string is given by

1. 1/n=1/n₁+1/n₂+1/n₃
 

2. 1/√n=1/√n₁+1/√n₂+1/√n₃

3. √n=√n₁+√n₂+√n₃

4. n=n₁+n₂+n₃

A speed motorcyclist sees a traffic jam ahead of him. He slows down to 36km/h. He finds that traffic has eased and a car moving in front of him at 18km/h is honking at a frequency of 1392Hz. If the speed of sound is 343m/s, the frequency of the honk as heard by him will be 
1. 1332Hz
2. 1372Hz
3. 1412Hz
4. 1454Hz 

A wave travelling in the positive x-direction having maximum displacement along y-direction as 1m, wavelength 2π m and frequency of 1/π Hz is represented by

1. y=sin(x-2t)
2. y=sin(2πx-2πt)
3. y=sin(10πx-20πt)
4. y=sin(2πx+2πt)

If we study the vibration of a pipe open at both ends. then the following statements is not true

1. Open end will be anti-node

2. Odd harmonics of the fundamental frequency will be generated

3. All harmonics of the fundamental frequency will be generated

4. Pressure change will be maximum at both ends

A source of unknown frequency gives 4 beats/s when sounded with a source of known frequency 250 Hz. The second harmonic of the source of unknown frequency gives five beats per second when sounded with a source of frequency 513 Hz. The unknown frequency is

1. 254 Hz

2. 246 Hz

3. 240 Hz

4. 260 Hz