Pressure Wave Derivation

Q.

If equation of sound wave is $\mathrm{y}=0.0015\sin \left(62.4\mathrm{x}+316\mathrm{t}\right)$, then its wavelength will be ______.

Q. Pressure equation of a sound wave is $P=0.02\sin (3000t-9x)$ where all quantities are in $\text{SI}$ unit. The frequency and speed of sound wave is

1. $\frac{1000}{\pi }\text{Hz},500\text{m/s}$
2. $\frac{1500}{\pi }\text{Hz},\frac{1000}{3}\text{m/s}$
3. $100\pi \text{Hz},250\text{m/s}$
4. $200\pi \text{Hz},500\text{m/s}$

Q. Below figure represents the displacement y versus distance x along the direction of propagation of a longitudinal wave. The pressure is maximum at position marked

1. P
2. Q
3. R
4. S

Q.

The equation of a sound wave in air is given by

$p=\left(0.01N{m}^{-2}\right)sin\left[\right(1000s^{-1})t-(3.0m^{-1}\left)x\right]$

(a) Find the frequency, wavelength and the speed of sound wave in air.

(b) If the equilibrium pressure of air is $1.0\times {10}^{5}N{m}^{-2}$, what are the maximum and minimum pressures at a point as the wave passes through that point.

$$\begin{array}{cc}& \\ \left(i\right)2.1& \left(p\right)\text{frequency in Hz}\\ \left(ii\right)1.0\times {10}^5+0.01& \left(q\right)\text{wavelength in m}\\ \left(iii\right)333& \left(r\right)\text{speed in m/s}\\ \left(iv\right)160& \left(s\right)\text{Max p in}N{m}^{-2}\end{array}$$

1. (p) - (iv); (q) - (i); (r) - (iii); (s) - (ii); (t) - (v)
2. (p) - (i); (q) - (ii); (r) - (iii); (s) - (iv); (t) - (v)
3. (p) - (iv); (q) - (v); (r) - (iii); (s) - (ii); (t) - (i)
4. (p) - (v); (q) - (ii); (r) - (i); (s) - (iii); (t) - (iv)

Q. A man observed the pressure amplitude in a sound wave from a wireless receiver as $4\times {10}^{-2}{\text{N/m}}^2$ and the intensity at a point as ${10}^{-6}{\text{W/m}}^2$. If by turning the volume knob, the pressure amplitude is increased to $5\times {10}^{-2}{\text{N/m}}^2$, evaluate the intensity.

1. ${10}^{-6}{\text{W/m}}^2$
2. $1.25\times {10}^{-6}{\text{W/m}}^2$
3. $1.56\times {10}^{-6}{\text{W/m}}^2$
4. $2\times {10}^{-6}{\text{W/m}}^2$

Q. A sound wave of wavelength $50\text{cm}$ travels in a gas medium. If the difference between the maximum and minimum pressures at a given point is $5\times {10}^{-3}{\text{N/m}}^2$ and the amplitude of vibration of the particles of the medium is $5\times {10}^{-10}\text{m}$, find bulk modulus of the medium.

Q.

For sound waves in air with frequency 1000 Hz, a displacement amplitude of $1.2\times {10}^{-8}$ m produces a pressure amplitude of $3.0\times {10}^{-2}$ Pa. What is the wavelength of these waves? (Provided Bulk modulus of Air = $1.42\times {10}^{5}Pa$)

1. 0.3 m

2. 0.4 m

3. 0.36 m

4. None of these

Q.

The equation of a sound wave in air is given by

$p=\left(0.01N{m}^{-2}\right)sin\left[\right(1000s^{-1})t-(3.0m^{-1}\left)x\right]$

(a) Find the frequency, wavelength and the speed of sound wave in air.

(b) If the equilibrium pressure of air is $1.0\times {10}^{5}N{m}^{-2}$, what are the maximum and minimum pressures at a point as the wave passes through that point.

$$\begin{array}{cc}& \\ \left(i\right)2.1& \left(p\right)\text{frequency in Hz}\\ \left(ii\right)1.0\times {10}^5+0.01& \left(q\right)\text{wavelength in m}\\ \left(iii\right)333& \left(r\right)\text{speed in m/s}\\ \left(iv\right)160& \left(s\right)\text{Max p in}N{m}^{-2}\end{array}$$

1. (p) - (iv); (q) - (i); (r) - (iii); (s) - (ii); (t) - (v)
2. (p) - (i); (q) - (ii); (r) - (iii); (s) - (iv); (t) - (v)
3. (p) - (iv); (q) - (v); (r) - (iii); (s) - (ii); (t) - (i)
4. (p) - (v); (q) - (ii); (r) - (i); (s) - (iii); (t) - (iv)

Q. A sound wave is propagating through a medium and the displacement equation for the particles of the medium is given by $y=-A_0\sin (kx-\omega t)$ then which of the following options represents a possible pressure wave through this medium?

1. $\Delta P_o\sin (kx-\omega t)$
2. $\Delta P_o\cos (kx-\omega t)$
3. $-\Delta P_o\cos (kx-\omega t)$
4. $-\Delta P_o\cos (kx+\omega t)$

Q. A sound wave is propagating through a medium and the displacement equation for the particles of the medium is given by $y=-A_0\sin (kx-\omega t)$ then which of the following options represents a possible pressure wave through this medium?

1. $\Delta P_o\sin (kx-\omega t)$
2. $\Delta P_o\cos (kx-\omega t)$
3. $-\Delta P_o\cos (kx-\omega t)$
4. $-\Delta P_o\cos (kx+\omega t)$

Q.

Calculate the bulk modulus of air from the following data about a sound wave of wavelength 35 cm travelling in air. The pressure at a point varies between $(1.0\times {10}^{5}and14)$ Pa and the particles of the air vibrate in simple harmonic motion of amplitude $5.5\times {10}^{-6}$ m.

1. $3.2\times {10}^2\frac{N}{m^2}$

2. $5.5\times {10}^6\frac{N}{m^2}$

3. $1.4\times {10}^5\frac{N}{m^2}$

4. None of these

Q. For the pressure variation in a longitudinal wave represented as $P=P_o\cos (\omega t-kx)$, the density $\left(\rho \right)$ equation for the given medium is best represented by
(${\rho }_o$ is the density of the medium at pressure $P_o$)

1. $\rho ={\rho }_o\sin (\omega t-kx)$
2. $\rho =-{\rho }_o\sin (\omega t-kx)$
3. $\rho ={\rho }_o\cos (\omega t-kx)$
4. $\rho =-{\rho }_o\cos (\omega t-kx)$

Q.

Calculate the bulk modulus of air from the following data about a sound wave of wavelength 35 cm travelling in air. The pressure at a point varies between $(1.0\times {10}^{5}and14)$ Pa and the particles of the air vibrate in simple harmonic motion of amplitude $5.5\times {10}^{-6}$ m.

1. $3.2\times {10}^2\frac{N}{m^2}$

2. $5.5\times {10}^6\frac{N}{m^2}$

3. $1.4\times {10}^5\frac{N}{m^2}$

4. None of these