Two waves are represented by the equations \(y_1 = a\sin(\omega t+kx+0.57)~\text{m}\) and 
\(y_2 = a\cos(\omega t+kx)~\text{m},\) where \(x\) is in meters and \(t\) in seconds. The phase difference between them is:
1. \(1.25\) rad
2. \(1.57\) rad
3. \(0.57\) rad
4. \(1.0\) rad

A transverse wave is represented by y = Asin(ωt -kx). At what value of the wavelength is the wave velocity equal to the maximum particle velocity?

1. $\pi$A/2

2. $\pi$A

3. 2$\pi$A

4. A

A tuning fork of frequency \(512~\text{Hz}\) makes \(4~\text{beats/s}\) with the vibrating string of a piano. The beat frequency decreases to \(2~\text{beats/s}\) when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was:
1. \(510~\text{Hz}\) 
2. \(514~\text{Hz}\) 
3. \(516~\text{Hz}\) 
4. \(508~\text{Hz}\) 

The driver of a car travelling at a speed of 30 m/s towards a hill sounds a horn of frequency 600 Hz. If the velocity of sound in air is 330 m/s, the frequency of reflected sound as heard by the driver is:

1. 550 Hz

2. 555.5 Hz

3. 720 Hz

4. 500 Hz

The wave described by \(y=0.25\sin (10\pi x-2\pi t)\), where \(x \) and \(y\) are in metre and \(t\) in second, is a wave travelling along the:

Two sound waves with wavelengths \(5.0~\text{m}\) and \(5.5~\text{m}\), respectively, propagate in gas with a velocity of \(330~\text{m/s}\). How many beats per second can we expect?
1. \(12\)
2. \(0\)
3. \(1\)
4. \(6\)

A transverse wave propagating along the \(x\text-\)axis is represented by:
\(y(x,t)=8.0\sin\left(0.5\pi x-4\pi t-\frac{\pi}{4}\right)\), where \(x\) is in meters and \(t\) in seconds. The speed of the wave is: 
1. \(4\pi\) m/s
2. \(0.5\) m/s
3. \(\frac{\pi}{4}\) m/s
4. \(8\) m/s