A string is stretched between two rigid supports 100 cm apart. In the frequency range between 100 and 350 cps only the following frequencies can be excited: 160, 240, 320 cps. What is the wavelength of each of these modes of vibration?
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As the two ends of the string are fixed, we have n λ = 2L, where L is the length of the string and n an integer. Let the wavelengths corresponding to frequencies 160, 240, 320 Hz be λ 0 , λ 1 , λ 2 respectively. Then
n λ 0 = (n + 1) λ 1 = (n + 2) λ 2 = 200,
160 λ 0 = 240 λ 1 = 320 λ 2 .
Hence n = 2, and
λ 0 = 100 cm, λ 1 = 67 cm, λ 2 = 50 cm.
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