A bat emits an ultrasonic sound of frequency \(1000~\text{kHz}\) in the air. If the sound meets a water surface, what is the wavelength of the refracted sound?
(speed of sound in air is \(340~\mathrm{m/s}\) and in water \(1486~\mathrm{m/s}\))

1.	\(3.4 \times 10^{-4} \mathrm{~m} \)	2.	\(1.4 \times 10^{-3} \mathrm{~m} \)
3.	\(2.5 \times 10^{-4} \mathrm{~m} \)	4.	\(1.8 \times 10^{-3} \mathrm{~m}\)

A hospital uses an ultrasonic scanner to locate tumors in a tissue. What is the wavelength of sound in the tissue in which the speed of sound is \(1.7~\text{km/s}\)? The operating frequency of the scanner is \(4.2~\text{MHz}\).
1. \(3.0 \times10^{-4}~\text{m}\)
2. \(4.0 \times10^{-4}~\text{m}\)
3. \(3.5 \times10^{-4}~\text{m}\)
4. \(2.0 \times10^{-4}~\text{m}\)

A transverse harmonic wave on a string is described by, \(y(x,t) = 3.0 sin ( 36t + 0.018x + {\pi \over 4})\) where x and y are in cm and t in sec. The positive direction of x is from left to right. What is the shortest distance between two successive crests in the wave?

For the travelling harmonic wave, \(y(x,t) = 2.0\ cos\ 2\pi (10t - 0.0080x + 0.35 )\) where \(x\) and \(y\) are in \(\text{cm}\) and \(t\) is in seconds. The phase difference between the oscillatory motion of two points separated by a distance of \(4~\text{m}\) will be:
1. \(0.8 \pi\ \text{rad}\)
2.  \(\pi\ \text{rad}\)
3. \(6.4\pi\ \text{rad}\)
4. \(4\pi\ \text{rad}\)

A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of 45 Hz. The mass of the wire is $3.5\times {10}^{-2}$ kg and its linear mass density is$4.0\times {10}^{-2}$   kg/m. What is the speed of the transverse wave on the string?

1. 74.31 m/s
2. 75.70 m/s
3. 78.75 m/s
4. 72 m/s

A one-meter 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 Hz) when the minimum tube length is 25.5 cm. The speed of sound in air at the temperature of the experiment is: (The edge effects may be neglected.)

1. 324.16 m/s

2. 320 m/s

3. 345 m/s

4. 346.8 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 Hz beats. The tension in the string A is slightly reduced, and the beat frequency is found to be reduced to 3 Hz. If the original frequency of A is 324 Hz, what is the frequency of B?

1. 316 Hz

2. 318 Hz

3. 319 Hz

4. 314 Hz