A standing wave is produced on a string clamped at one end and free at the other. The length of the string:

1.	must be an integral multiple of \(\frac{\lambda}{4}\)
2.	must be an integral multiple of \(\frac{\lambda}{2}\)
3.	must be an integral multiple of \(\lambda\)
4.	may be an integral multiple of \(\frac{\lambda}{2}\)

Which of the following statement is correct?

In a stationary wave,

(a) all the particles of the medium vibrate in phase

(b) all the antinodes vibrate in phase

(c) the alternate antinodes vibrate in phase

(d) all the particles between consecutive nodes vibrate in phase

Choose the correct option:

1. (a) and (b)

2. (b) and (c)

3. (c) and (d)

4. all of these

Consider the following statements about sound passing through a gas.

When we clap our hands, the sound produced is best described by
(Here p denotes the change in pressure from the equilibrium value)

1. p = p₀ sin(kx – ωt)

2. p = p₀ sin kx cos ωt

3. p = p₀ cos kx sin ωt

4. p = \(\sum\)p_0n sin(k_nx – ω_nt)

The bulk modulus and the density of water are greater than those of air. With this much of information, we can say that velocity of sound in air

1. is larger than its value in water

2. is smaller than its value in water

3. is equal to its value in water

4. cannot be compared with its value in water

A tuning fork sends sound waves in the air. If the temperature of the air increases, which of the following parameters will change?

1. Displacement amplitude

2. Frequency

3. Wavelength

4. Time period

When sound wave is refracted from air to water, which of the following will remain unchanged?

1. Wave number

2. Wavelength

3. Wave velocity

4. Frequency

The speed of sound in a medium depends on:

Two sound waves move in the same direction in the same medium. The pressure amplitudes of the waves are equal but the wavelength of the first wave is double the second. Let the average power transmitted across cross-section by the first wave be \(P_1\) and that by the second wave be \(P_2.\) Then: