A tuning fork of frequency \(512~\text{Hz}\) makes \(4\) beats/s with the vibrating strings of a piano. The beat frequency decreases to \(2\) beats/s when the tension in the piano strings 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. \(508~\text{Hz}\)

A wave in a string has an amplitude of 2 cm. The wave travels in the +ve direction of x-axis with a speed of $128 {\mathrm{ms}}^{-1}$ and it is noted that 5 complete waves fit in 4 m length of the string. The equation describing the wave is :

(1) $y=\left(0.02\right)\mathrm{m} \sin \left(7.85\mathrm{x} +1005\mathit{ }t \right)$

(2) $y=\left(0.02\right)\mathrm{m} \sin \left(15.7\mathrm{x} -2010\mathit{ }t \right)$

(3) $y=\left(0.02\right)\mathrm{m} \sin \left(15.7\mathrm{x} +2010\mathit{ }t \right)$

(4) $y=\left(0.02\right)\mathrm{m} \sin \left(7.85\mathrm{x} -1005\mathit{ }t \right)$

Each of the two strings of length 51.6 cm and 49.1 cm are tensioned separately by 20N force. Mass per unit length of both the strings is same and equal to 1 $g{m}^{-1}$When both the strings vibrate simultaneously the number of beats is :

1. 5                                                   

2. 7

3. 8                                                   

4. 3

Two periodic waves of intensities $I_1 and I_2$ pass through a region at the same time in the same direction. The sum of the maximum and  minimum intensities is :

(1) $I_1+I_2$

(2) ${\left(\sqrt{I_1}+\sqrt{I_2}\right)}^2$

(3)${\left(\sqrt{I_1}-\sqrt{I_2}\right)}^2$

(4) $2 \left(I_1+I_2\right)$ 

Two points are located at a distance of 10 m and 15 m from the source of oscillation. The period of oscillation is 0.05 s and the velocity of the wave is 300 m/s. What is the phase difference between the oscillations of two points?

(1) $\frac{\pi }{3}$

(2) $\frac{2\pi }{3}$

(3) $\pi$

(4) $\frac{\pi }{6}$

Two waves are represented by the equations $y_1=a\sin \omega t$ and $y_2=a\cos \omega t.$ The first wave 

(1) Leads the second by $\pi$

(2) Lags the second by $2\pi$

(3) Leads the second by $\frac{\pi }{2}$

(4) Lags the second by $\frac{\pi }{2}$

The distance between two consecutive crests in a wave train produced in a string is 5 cm. If 2 complete waves pass through any point per second, the velocity of the wave is :

1. 10 cm/sec

2. 2.5 cm/sec

3. 5 cm/sec

4. 15 cm/sec

A tuning fork makes 256 vibrations per second in air. When the velocity of sound is 330 m/s, then the wavelength of the tone emitted is :

1. 0.56 m

2. 0.89 m

3. 1.11 m

4. 1.29 m

Sound waves have the following frequencies that are audible to human beings :

1. 5 c/s

2. 27000 c/s

3. 5000 c/s

4. 50,000 c/s