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A metal rod of 1m length, is dropped exact vertically on to a hard metal floor. With an oscilloscope, it is determined that the impact produces a longitudinal wave of 1.2 kHz frequency. The speed of sound in the metal rod is?
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A metal rod of 1m length, is dropped exact vertically on to a hard met...

Speed of Sound in Metal Rod Calculation

Given Data:
- Length of metal rod (L) = 1m
- Frequency of longitudinal wave (f) = 1.2 kHz = 1200 Hz

Formula:
Speed of sound (v) = f * λ

Calculations:
- First, we need to find the wavelength (λ) of the longitudinal wave.
- Wavelength is the distance between two consecutive compressions or rarefactions in the wave.
- In this case, the metal rod is fixed at one end (floor) and free at the other end (dropped vertically).
- Therefore, the rod will produce a longitudinal wave with one antinode (open end) and one node (fixed end).

Using the formula for the fundamental frequency of a closed-open tube:
λ = 4L

Substitute the values:
λ = 4 * 1m = 4m

Now, calculate the speed of sound in the metal rod:
v = f * λ
v = 1200 Hz * 4m
v = 4800 m/s

Answer:
The speed of sound in the metal rod is 4800 m/s.
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A metal rod of 1m length, is dropped exact vertically on to a hard metal floor. With an oscilloscope, it is determined that the impact produces a longitudinal wave of 1.2 kHz frequency. The speed of sound in the metal rod is?
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