Question

1. a transverse progressive wave on a stretched string has a speed of 40 m/s and a frequency of 100 hz. the phase difference, at any instant, between two points on the string which are 2.5 cm apart. is

a. π
b. π/4
c. π/2
d. 3π/8

1. two sound waves are y = asin(ωt - kx) and y = acos(ωt - kx). the phase difference between the two waves is

a. π/2
b. π/4
c. π
d. 0

1. ultrasonic waves are those waves which

a. human beings cannot hear
b. human beings can hear
c. have high velocity
d. have large amplitude

Explanation:

1. For question 12:

• # Explanation:
• ## Step1: Find the wavelength
• We know that \(v = f\lambda\), where \(v = 10\ m/s\) and \(f = 100\ Hz\). So, \(\lambda=\frac{v}{f}=\frac{10}{100}=0.1\ m = 10\ cm\).
• ## Step2: Calculate the phase difference
• The formula for phase difference \(\Delta\phi=\frac{2\pi}{\lambda}\Delta x\). Given \(\Delta x = 2.5\ cm\) and \(\lambda = 10\ cm\). Then \(\Delta\phi=\frac{2\pi}{10}\times2.5=\frac{\pi}{2}\).
• # Answer:
• C. \(\frac{\pi}{2}\)

1. For question 13:

• # Explanation:
• ## Step1: Use trigonometric identity
• We know that \(A\cos(\omega t - kx)=A\sin(\omega t - kx+\frac{\pi}{2})\).
• ## Step2: Find the phase difference
• For \(y = A\sin(\omega t - kx)\) and \(y = A\cos(\omega t - kx)=A\sin(\omega t - kx+\frac{\pi}{2})\), the phase difference \(\Delta\phi=\frac{\pi}{2}\).
• # Answer:
• A. \(\frac{\pi}{2}\)

1. For question 14:

• # Brief Explanations:
• Ultrasonic waves have a frequency greater than \(20000\ Hz\). The audible range for human beings is \(20 - 20000\ Hz\). So, human beings cannot hear ultrasonic waves.
• # Answer:
• A. human beings cannot hear

Answer:

1. For question 12:

• # Explanation:
• ## Step1: Find the wavelength
• We know that \(v = f\lambda\), where \(v = 10\ m/s\) and \(f = 100\ Hz\). So, \(\lambda=\frac{v}{f}=\frac{10}{100}=0.1\ m = 10\ cm\).
• ## Step2: Calculate the phase difference
• The formula for phase difference \(\Delta\phi=\frac{2\pi}{\lambda}\Delta x\). Given \(\Delta x = 2.5\ cm\) and \(\lambda = 10\ cm\). Then \(\Delta\phi=\frac{2\pi}{10}\times2.5=\frac{\pi}{2}\).
• # Answer:
• C. \(\frac{\pi}{2}\)

1. For question 13:

• # Explanation:
• ## Step1: Use trigonometric identity
• We know that \(A\cos(\omega t - kx)=A\sin(\omega t - kx+\frac{\pi}{2})\).
• ## Step2: Find the phase difference
• For \(y = A\sin(\omega t - kx)\) and \(y = A\cos(\omega t - kx)=A\sin(\omega t - kx+\frac{\pi}{2})\), the phase difference \(\Delta\phi=\frac{\pi}{2}\).
• # Answer:
• A. \(\frac{\pi}{2}\)

1. For question 14:

• # Brief Explanations:
• Ultrasonic waves have a frequency greater than \(20000\ Hz\). The audible range for human beings is \(20 - 20000\ Hz\). So, human beings cannot hear ultrasonic waves.
• # Answer:
• A. human beings cannot hear