A 2-m long string is stretched between two supports with a tension that produces a wave speed equal to 50.00 m/s. What are the wavelength and frequency of the first three modes that resonate on the string?

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Chapter16: Waves
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Problem 27CQ: Many of the topics discussed in this chapter are useful beyond the topics of mechanical waves. It is...
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Professor Sathya Swaroop
Problem Set 2 [Module 1]
1.
A 2-m long string is stretched between two supports with a tension that produces a wave speed equal to 50.00 m/s. What
are the wavelength and frequency of the first three modes that resonate on the string?
2.
Consider two wave functions y,(x, t) = (0.3 cm) sin(3.00m-1 x – 4.00s- t) and y2(x, t) = (0.3 cm) sin(3.00m- x +
%3D
4.00s-1 t). Write a wave function for the resulting standing wave.
3.
Two sinusoidal waves with identical wavelengths and amplitudes travel in opposite directions along a string producing a
standing wave. The linear mass density of the string is 0.075 kg/m and the tension in the string is 5.00 N. The time interval
between instances of total destructive interference is 0.13 s. What is the wavelength of the waves?
4.
The frequencies of two successive modes of standing waves on a string are 258.36 Hz and 301.42 Hz. What is the next
frequency above these two frequencies that would produce a standing wave?
5.
Sine waves are sent down a 1.5m long string fixed at both ends. The waves reflect back in the opposite direction. The
amplitude of the wave is 4.00 cm. The propagation velocity of the waves is 175 m/s. The sixth harmonics of the string is
produced. Write an equation for the resulting standing wave.
Transcribed Image Text:Professor Sathya Swaroop Problem Set 2 [Module 1] 1. A 2-m long string is stretched between two supports with a tension that produces a wave speed equal to 50.00 m/s. What are the wavelength and frequency of the first three modes that resonate on the string? 2. Consider two wave functions y,(x, t) = (0.3 cm) sin(3.00m-1 x – 4.00s- t) and y2(x, t) = (0.3 cm) sin(3.00m- x + %3D 4.00s-1 t). Write a wave function for the resulting standing wave. 3. Two sinusoidal waves with identical wavelengths and amplitudes travel in opposite directions along a string producing a standing wave. The linear mass density of the string is 0.075 kg/m and the tension in the string is 5.00 N. The time interval between instances of total destructive interference is 0.13 s. What is the wavelength of the waves? 4. The frequencies of two successive modes of standing waves on a string are 258.36 Hz and 301.42 Hz. What is the next frequency above these two frequencies that would produce a standing wave? 5. Sine waves are sent down a 1.5m long string fixed at both ends. The waves reflect back in the opposite direction. The amplitude of the wave is 4.00 cm. The propagation velocity of the waves is 175 m/s. The sixth harmonics of the string is produced. Write an equation for the resulting standing wave.
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