Correct answer Carries: 4.
Wrong Answer Carries: -1.
What is the significance of the beat frequency when two sound waves interfere?
The beat frequency, \( |f_1 - f_2| \), is the rate at which amplitude modulates, perceived as periodic loudness variations, equal to the difference in wave frequencies.
A longitudinal wave in a medium has a speed of 1500 m/s and a density of 1200 kg/m³. What is the bulk modulus of the medium?
Speed: \( v = \sqrt{\frac{B}{\rho}} \).
\( 1500 = \sqrt{\frac{B}{1200}} \Rightarrow 1500^2 = \frac{B}{1200} \).
\( B = 1500^2 \times 1200 = 2.7 \times 10^9 \, \text{Pa} \).
What type of wave is produced when a stone is dropped into a still pond?
A stone dropped into a pond creates ripples that oscillate perpendicular to the direction of propagation on the surface, forming transverse waves, specifically gravity waves for larger wavelengths.
A longitudinal wave in a medium has a speed of 1700 m/s and a bulk modulus of 2.89 × 10⁹ Pa. What is the density of the medium?
\( 1700 = \sqrt{\frac{2.89 \times 10^9}{\rho}} \Rightarrow 1700^2 = \frac{2.89 \times 10^9}{\rho} \).
\( \rho = \frac{2.89 \times 10^9}{1700^2} = \frac{2.89 \times 10^9}{2.89 \times 10^6} = 1000 \, \text{kg/m}^3 \).
What is the physical basis for the formation of beats in sound waves?
Beats arise from the superposition of two waves with slightly different frequencies, causing periodic constructive and destructive interference, perceived as amplitude variation.
A pipe open at both ends has a length of 0.51 m and a speed of sound of 340 m/s. What is the frequency of its third harmonic?
For open pipe: \( v_n = \frac{n v}{2L} \).
Third harmonic (\( n = 3 \)): \( v_3 = \frac{3 \times 340}{2 \times 0.51} = \frac{1020}{1.02} = 1000 \, \text{Hz} \).
A wave is described by \( y(x, t) = 0.06 \sin (30x - 90t) \), where \( x \) and \( y \) are in meters and \( t \) in seconds. What is the wave speed?
Compare with \( y = a \sin (kx - \omega t) \).
\( k = 30 \, \text{rad/m} \), \( \omega = 90 \, \text{rad/s} \).
Speed: \( v = \frac{\omega}{k} = \frac{90}{30} = 3 \, \text{m/s} \).
What is the key difference between a progressive wave and a standing wave?
A progressive wave transfers energy through the medium as it propagates, while a standing wave has fixed nodes and antinodes with no net energy transfer, only oscillation.
A pipe closed at one end has a length of 0.25 m and resonates at its fundamental frequency with a speed of sound of 340 m/s. What is the frequency?
Fundamental: \( v_1 = \frac{v}{4L} \).
\( v_1 = \frac{340}{4 \times 0.25} = \frac{340}{1} = 340 \, \text{Hz} \).
A longitudinal wave in a medium has a speed of 1550 m/s and a density of 1200 kg/m³. What is the bulk modulus of the medium?
\( 1550 = \sqrt{\frac{B}{1200}} \Rightarrow 1550^2 = \frac{B}{1200} \).
\( B = 1550^2 \times 1200 = 2.88 \times 10^9 \, \text{Pa} \).
Are you sure you want to submit your answers?
