Multiple Choice
A standing wave on a string in the mode has a frequency of What is the frequency of the standing wave?
18. Waves & Sound
Standing Waves
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A 3m-long rope is stretched between two supports with a tension that makes the speed of transverse waves 60 m/s. What are the wavelength and frequency of the second overtone?
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Verified step by step guidance1
Identify the length of the rope, which is given as 3 meters. This is the distance between the two supports.
Understand that the second overtone corresponds to the third harmonic in a stretched string. For the third harmonic, the string supports 3 half-wavelengths.
Calculate the wavelength for the third harmonic using the formula: \( \lambda = \frac{2L}{n} \), where \( L \) is the length of the rope and \( n \) is the harmonic number. Here, \( n = 3 \).
Substitute the given values into the wavelength formula: \( \lambda = \frac{2 \times 3}{3} \).
Use the wave speed formula \( v = f \lambda \) to find the frequency \( f \). Given the wave speed \( v = 60 \text{ m/s} \) and the calculated wavelength, solve for \( f \) using \( f = \frac{v}{\lambda} \).
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