Correct answer Carries: 4.
Wrong Answer Carries: -1.
A string of length 1.8 m and mass 0.045 kg has a fundamental frequency of 40 Hz. What is the tension in the string?
\( \mu = \frac{0.045}{1.8} = 0.025 \, \text{kg/m} \).
\( v_1 = \frac{v}{2L} \Rightarrow 40 = \frac{v}{2 \times 1.8} \Rightarrow v = 40 \times 3.6 = 144 \, \text{m/s} \).
\( v = \sqrt{\frac{T}{\mu}} \Rightarrow 144 = \sqrt{\frac{T}{0.025}} \Rightarrow 144^2 = \frac{T}{0.025} \).
\( T = 20736 \times 0.025 = 518.4 \, \text{N} \).
A pipe closed at one end has a length of 0.5 m and resonates at its fundamental frequency with a speed of sound of 350 m/s. What is the frequency?
Fundamental: \( v_1 = \frac{v}{4L} \).
\( v_1 = \frac{350}{4 \times 0.5} = \frac{350}{2} = 175 \, \text{Hz} \).
A pipe open at both ends has a length of 0.85 m and a speed of sound of 340 m/s. What is the frequency of its first harmonic?
For open pipe: \( v_n = \frac{n v}{2L} \).
First harmonic (\( n = 1 \)): \( v_1 = \frac{340}{2 \times 0.85} = \frac{340}{1.7} = 200 \, \text{Hz} \).
A string fixed at both ends has a length of 2 m and a wave speed of 90 m/s. What is the frequency of its third harmonic?
For fixed ends: \( v_n = \frac{n v}{2L} \).
Third harmonic (\( n = 3 \)): \( v_3 = \frac{3 \times 90}{2 \times 2} = \frac{270}{4} = 67.5 \, \text{Hz} \).
A stationary wave on a string fixed at both ends has a frequency of 100 Hz and a wave speed of 40 m/s. What is the length of the string?
Fundamental: \( v_1 = \frac{v}{2L} \).
\( 100 = \frac{40}{2L} \Rightarrow 2L = \frac{40}{100} \Rightarrow 2L = 0.4 \Rightarrow L = 0.2 \, \text{m} \).
Two waves of frequencies 465 Hz and 470 Hz interfere. How many beats are heard in 12 seconds?
Beat frequency: \( v_{\text{beat}} = 470 - 465 = 5 \, \text{Hz} \).
Beats in 12 s: \( 5 \times 12 = 60 \).
A transverse wave on a string has a speed of 30 m/s and a wavelength of 1.5 m. What is the time period of the wave?
Speed: \( v = v \lambda \), \( v = \frac{v}{\lambda} = \frac{30}{1.5} = 20 \, \text{Hz} \).
Time period: \( T = \frac{1}{v} = \frac{1}{20} = 0.05 \, \text{s} \).
A wave \( y = 0.04 \sin (30x - 60t) \) reflects at an open boundary. What is the equation of the reflected wave?
At open boundary, no phase change.
Incident: \( y_i = 0.04 \sin (30x - 60t) \).
Reflected: \( y_r = 0.04 \sin (30x + 60t) \).
A wave on a string has an amplitude of 0.02 m and a period of 0.01 s. What is the maximum transverse speed of a particle?
\( \omega = \frac{2\pi}{T} = \frac{2\pi}{0.01} = 200\pi \, \text{rad/s} \).
Max speed: \( v_{\text{max}} = a \omega = 0.02 \times 200\pi \approx 12.57 \, \text{m/s} \).
A transverse wave on a string has a speed of 24 m/s and a period of 0.02 s. What is its wavelength?
Frequency: \( v = \frac{1}{T} = \frac{1}{0.02} = 50 \, \text{Hz} \).
Wavelength: \( \lambda = \frac{v}{v} = \frac{24}{50} = 0.48 \, \text{m} \).
Are you sure you want to submit your answers?
