a metal of 50cm length when dropped rebounds from the surface causing waves of speed 5500m/s the lowest frequency to which the rod resonates while rebounding is

To determine the lowest frequency at which a metal rod resonates after being dropped and rebounding, we can use the relationship between the speed of sound in the material, the length of the rod, and the frequency of the fundamental mode of vibration. The fundamental frequency is the lowest frequency at which the rod can vibrate, and it can be calculated using the formula:

Understanding the Relationship

The fundamental frequency (f) of a vibrating rod can be expressed as:

f = v / λ

Where:

• f = frequency in hertz (Hz)
• v = speed of sound in the material (m/s)
• λ = wavelength (m)

Calculating Wavelength

For a rod fixed at both ends, the wavelength of the fundamental mode is twice the length of the rod:

λ = 2L

In this case, the length (L) of the rod is 50 cm, which we need to convert to meters:

L = 50 cm = 0.5 m

Now, substituting this into the wavelength formula gives:

λ = 2 * 0.5 m = 1 m

Finding the Frequency

Now that we have the wavelength, we can substitute the values into the frequency formula. The speed of sound in the metal is given as 5500 m/s:

f = 5500 m/s / 1 m = 5500 Hz

Final Result

The lowest frequency at which the rod resonates while rebounding is therefore:

5500 Hz

This means that when the rod rebounds, it will vibrate at this fundamental frequency, producing sound waves at 5500 Hz. This frequency is characteristic of the material and dimensions of the rod, illustrating how physical properties influence vibrational behavior.