A steel rod 100 cm long is clamped at its middle. The fundamental frequency of longitudinal vibrations of the rod is given to be 2.53 kHz. What is the speed of sound in steel?
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Answered by
7
Hey
So, the rod is clamped at its middle (given)
∴ It has one antinode and two nodes now.
fundamental frequency of longitudinal vibrations (v) = 2.53 kHz
v = 2.53 × 13^3 Hz.
rod = 100 cm long
The length between the two nodes = wavelength/ 2
wavelength = 2 × length
= 2 × 100 = 200 cm / 2 m.
The speed of sound in steel?
= wavelength × frequency of longitudinal vibrations
= 2 m × 2.53 × 13^3
= 5.06 × 10^3 m/s.
= 5.06 km/s
The speed of sound in steel = 5.06 km/s.
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Hope this helps!
So, the rod is clamped at its middle (given)
∴ It has one antinode and two nodes now.
fundamental frequency of longitudinal vibrations (v) = 2.53 kHz
v = 2.53 × 13^3 Hz.
rod = 100 cm long
The length between the two nodes = wavelength/ 2
wavelength = 2 × length
= 2 × 100 = 200 cm / 2 m.
The speed of sound in steel?
= wavelength × frequency of longitudinal vibrations
= 2 m × 2.53 × 13^3
= 5.06 × 10^3 m/s.
= 5.06 km/s
The speed of sound in steel = 5.06 km/s.
-------------------------------------------------------------------------------------------------
.
.
.
.
.
.
Hope this helps!
Answered by
6
When a metal clamped at the middle will produced node at the centre and antinodes at open ends in fundamental and higher modes .
Length of rod ( L) =2( lemda/4)
= lemda/2
Here,
L = 100 cm , f = 2.53 kHz
So, wavelength ( lemda) = 200 cm
= 2m
velocity of wave = frequency × wavelength
= 2.53 × 10³ × 2 m/s
= 5.06 km/s
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