Physics M.C.Q (1 Marks)

1. 506Hz

Explanation:

The frequency of the sonometer may be $512\pm6\text{Hz},$ i.e., $506\text{Hz}$ or $518\text{Hz}.$

On increasing the tension in a sonometer wire, the velocity of the wave (v) increases proportionately as the number of beats decreases. Therefore, the frequency of the sonometer wire is 506Hz.

4. Separation between the source and the observer.

Explanation:

$\text{v}_0=\Big(\frac{\text{v}\pm\mu_0}{\text{v}\pm\mu_\text{s}}\Big)\text{v}_\text{B}$

It is clear from the equation that the chage in frequency due to Doppler effect depends only on the relative and not on the distance between the source and the observer.

3. $\text{v}$

Explanation:

If v is the velocity of the wave and L is the length of the pipe. then the fundamental frequency for an open pipe is:

$\text{v}=\frac{\text{v}}{2\text{L}}$

For a closed organ pipe of length of lenth $\text{L}'=\frac{\text{L}}{2},$ the fundamental frequency is:

$\text{v}=\frac{\text{v}}{4\text{L}'}=\frac{\text{v}\times2}{4\times\text{L}}=\frac{\text{v}}{2\text{L}}=\text{v}$

(When the pipe is dipped in water, it behaves like a closed pipe that is half the lenth)

4. $\text{p}=\sum\text{p}_{0\text{n}}\sin(\text{k}_\text{n}\text{x}-\omega_\text{n}\text{t}).$

Explanation:

When we clap, there is a change in pressure, which sets a disturbance and forms a wave. However, this variation is not uniform every time we clap (unlike in the case of a sound wave). Hence, we sum up all the disturbances.

1. Larger wavelength.

3. Larger velocity.

Explanation:

The velocity varies with temperature as $\text{v}\propto\sqrt{\text{T}}.$ Therefore, it increases. Since the frequency remains constant, the wavelength will increase as $\lambda\propto\text{v}.$

1. Frequency.

4. Time period.

Explanation:

The frequency does not change. Hence, the time period (inverse of frequency) also remains the same. Due to wind, the relative velocity of sound changes. Thus, the wavelength also changes so as to keep the frequency the same. $(\text{As}\ \nu=\nu\lambda)$

4. $\text{v}$

Explanation:

For the Doppler effect to occur, there must be relative motion between the source and the observer.

However, this is not the case here. Hence, the frequency heard by the passenger is v.

2. The first overtone may be 400Hz.
3. The first overtone may be 600Hz.
4. 600Hz is an overtone.

Explanation:

For an open organ pipe:

$\nu_\text{n}=\text{n}\text{v}_1$

n^th harmonic = (n - 1 )^th overtone

$\nu_1=200\text{Hz},\ \nu_2=400\text{Hz},\ \nu_3=600\text{Hz}$

If the pipe is an open organ pipe, then the 1^st overtone is 400Hz. Option (b) is correct.

Also, $\nu_3=600\text{Hz},$ i.e., second overtone = 600Hz.

600Hz is an overtone. Therefore, option (d) is correct.

If the pipe is a closed organ pipe, then $\nu_\text{n}=(2\text{n}-1)\nu_1.$

(2n - 1)^th harmonic = (n - 1)^th overtone

For n = 2

1^st overtone= 3^rd harmonic $=3\nu_1$

$=3\times200$

$=600\text{Hz}$

Therefore, option (c) is also correct.

3. Wavelength.

Explanation:

The velocity of a sound wave varies with temperature as follows:

$\text{v}\propto\sqrt{\text{T}}$

As the temperature increases, the speed also increases. However, since the frequency remains the same, its wavelength changes.

4. Cannot be compared with its value in water.

Explanation:

If B is the bulk modulus and pis the density, then the velocity of sound is given by:

Velocity $=\sqrt{\frac{\text{B}}{\rho}}$

If both Band p are greater, then we cannot compare $\frac{2\text{B}}{2\rho}=\frac{3\text{B}}{3\rho}=\frac{\text{B}}{\rho}.$

For proper comparison, we need numerical values.