A \(1~\text m,\) long tube open at one end with a movable piston at the other end shows resonance with a fixed frequency source (a tuning fork of frequency \(340~\text{Hz}\)) when the minimum tube length is \(25.5~\text{cm}.\) The speed of sound in air at the temperature of the experiment is:
(The edge effects may be neglected.)
1. \(324.16~\text{m/s}\)
2. \(320~\text{m/s}\) 
3. \(345~\text{m/s}\)
4. \(346.8~\text{m/s}\)

A steel rod \(100\) cm long is clamped at its middle. The fundamental frequency of the longitudinal vibrations of the rod is given to be \(2.53\) kHz. What is the speed of sound in steel?
1. \(5.06\) km/s
2. \(5.12\) km/s
3. \(4.29\) km/s
4. \(4.01\) km/s

Two sitar strings, \(A\) and \(B,\) playing the note \(Ga,\) are slightly out of tune and produce \(6~\text{Hz}\) beats. The tension in the string \(A\) is slightly reduced, and the beat frequency is found to be reduced to \(3~\text{Hz}\). If the original frequency of \(A\) is \(324~\text{Hz}\), what is the frequency of \(B\)?
1. \(316~\text{Hz}\)
2. \(318~\text{Hz}\)
3. \(319~\text{Hz}\)
4. \(314~\text{Hz}\)

A train, standing at the outer signal of a railway station blows a whistle of frequency \(400\) Hz in still air. What is the frequency of the whistle for a platform observer when the train approaches the platform with a speed of \(10\) m/s?
(Speed of sound\(=340\) m/s)
1. \(512 \) Hz
2. \(312 \) Hz
3. \(412\) Hz
4. \(400\) Hz

A train, standing in a station yard, blows a whistle of frequency 400 Hz in still air. The wind starts blowing in the direction from the yard to the station with a speed of 10 m/sec. What is the speed of sound for an observer standing on the station’s platform?

1. 332 m/s

2. 360 m/s

3. 344 m/s

4. 350 m/s

A traveling harmonic wave on a string is described by \(y(x,t) = 7.5 ~\mathrm{sin}(0.0050x+12t+\frac{\pi}{4})\). What is the displacement of oscillation of a point at \(x=1 ~\text{cm}\) and \(t=1~\text{s}\)? (\(\sin(12.79)=0.22\))
1. \(1.66~\text{cm}\)
2. \(1.54~\text{cm}\)
3. \(1.39~\text{cm}\)
4. \(1.29~\text{cm}\)

A SONAR system fixed in a submarine operates at a frequency 40.0 kHz. An enemy submarine moves towards the SONAR with a speed of 360 km/h. What is the frequency of sound reflected by the enemy submarine? (the speed of sound in water to be 1450 m/sec.)

(1) 44.2 kHz

(2) 45.9 kHz

(3) 43.7 kHz

(4) 46.1 kHz

Earthquakes generate sound waves inside the earth. Unlike a gas, the earth can experience both transverse (S) and longitudinal (P) sound waves. Typically the speed of the S wave is about 4.0 km/s, and that of the P waves is 8.0 km/s. A seismograph records P and S waves from an earthquake. The first P wave arrives 4 min before the first S wave. Assuming the waves travel in a straight line, at what distance does the earthquake occur?

1. 1854 km
2. 2320 km
3. 1920 km
4. 2000 km

A bat is flitting about in a cave, navigating via ultrasonic beeps. Assume that the sound emission frequency of the bat is 40 kHz. During one fast swoop directly toward a flat wall surface, the bat moves at 0.03 times the speed of sound in the air. What frequency does the bat hear reflected off the wall?

1. 41.27 kHz

2. 42.67 kHz

3. 41.23 kHz

4. 42.47 kHz

Which of the following phenomenon cannot take place with sound waves?

(1) Polarisation

(2) Refraction

(3) Diffraction

(4) Reflection