Question
Download Solution PDFA string 2.0 m long and fixed at its ends is driven by a 240 Hz vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Wave speed:
The speed of the wave is given by,
Wave speed = frequency × wavelength.
v = fλ
Wavelength (λ) is the distance between two corresponding points on adjacent waves. Wave frequency (f) is the number of waves that pass a fixed point in a given amount of time.
Fundamental Frequency:
The lowest frequency of any vibrating object is called the fundamental frequency.
i.e. the lowest frequency which is produced by the oscillation i.e., the fundamental frequency is given as,
Calculation:
Given,
Frequency, f = 240 Hz
Length of the string, l = 2 m
The string vibrates in third harmonic mode i.e., n = 3
Standing waves of many different wavelengths can be produced on a string with two fixed ends, as long as an integral number of half wavelengths fits into the length of the string.
For a standing wave on a string of length L with two fixed ends, its wavelength will be
The speed of the wave is given by,
Velocity,
By fundamental frequency formula,
The speed of the wave and its fundamental frequency is 320 m/sec and 80 Hz respectively.
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