A sonometer wire having a length of 50 cm is vibrating in the fundamental mode with a frequency of 100 Hz. Which of the following is the type of propagating wave and its peed?

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Q: 70 (NDA-I/2009)
A sonometer wire having a length of 50 cm is vibrating in the fundamental mode with a frequency of 100 Hz.
Which of the following is the type of propagating wave and its peed?

question_subject: 

Maths

question_exam: 

NDA-I

stats: 

0,0,10,6,2,2,0

keywords: 

{'wave': [0, 0, 1, 0], 'sonometer wire': [0, 0, 1, 0], 'fundamental mode': [0, 0, 1, 0], 'transverse': [0, 0, 1, 0], 'frequency': [0, 0, 1, 3], 'longitudinal': [0, 0, 1, 0], 'hz': [0, 0, 4, 8], 'type': [5, 0, 3, 14]}

The correct answer is option 4, Transverse, 100 m/s.

In a sonometer wire vibrating in the fundamental mode, the wave that is being propagated is a transverse wave. This type of wave oscillates perpendicular to the direction of its propagation. The vibrations in a transverse wave occur in a direction perpendicular to the direction of the wave.

The speed of a wave can be calculated using the formula:

Speed = Frequency x Wavelength

Here, we are given that the sonometer wire is vibrating at a frequency of 100 Hz. In the fundamental mode, the wavelength is twice the length of the wire. So, the wavelength would be 50 cm x 2 = 100 cm.

However, to determine the speed of the wave, we need to convert cm to m. So, the wavelength is 100 cm / 100 = 1 m.

Using the formula for speed, we have:

Speed = 100 Hz x 1 m = 100 m/s.

Therefore, the correct answer is option 4, Transverse, 100 m/s.