The standing wave pattern along a string of length 60 cm is shown in the below diagram. If the speed of the transverse waves on this string is 300 m/ s. in which one of the following modes in the string vibrating?

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Q: 69 (NDA-I/2009)
The standing wave pattern along a string of length 60 cm is shown in the below diagram. If the speed of the transverse waves on this string is 300 m/ s. in which one of the following modes in the string vibrating?

question_subject: 

Maths

question_exam: 

NDA-I

stats: 

0,4,4,1,1,4,2

keywords: 

{'transverse waves': [0, 0, 1, 0], 'standing wave pattern': [0, 0, 1, 0], 'string': [0, 0, 2, 2], 'modes': [1, 0, 1, 0], 'third overtone': [0, 0, 1, 0], 'second overtone': [0, 0, 1, 0], 'first overtone': [0, 0, 1, 0], 'below diagram': [0, 0, 2, 0], 'speed': [0, 1, 2, 0]}

The given problem involves a standing wave pattern on a string with a length of 60 cm and a speed of transverse waves on the string is 300 m/s.

To determine the mode in which the string is vibrating, we need to consider the relationship between the frequency of the wave and the length of the string.

In a string vibrating in a standing wave pattern, the length of the string is related to the wavelength of the wave. This relationship is given by the equation:

Length of string = (Number of nodes + Number of antinodes) * Wavelength / 2

In the given diagram, we can observe that there are two nodes and three antinodes. Plugging these values into the equation, we get:

60 cm = (2 + 3) * Wavelength / 2

Simplifying this equation, we find:

60 cm = 5/2 * Wavelength

Now, we can calculate the wavelength of the wave:

Wavelength = (60 cm * 2) / 5

= 24 cm

Using the formula for the frequency of a wave:

Frequency = Speed / Wavelength

= 300 m/s / (24 cm / 100 cm/m)

= 1250 Hz

Since