Question

➣Write and describe the Law of Vibration of the Stretched String
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Answer 1

Question:-

# Laws of Vibration of the Stretched String:-

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➣ There are 3 Laws:-

1. Laws of Length:- For a given string or wire under a given tension, the frequency of the string varies inversely as its vibrating length.

n directly proportional to 1/l

2. Laws of Tension:- For a uniform string of a given length and material the frequency of string is directly proportional to the square root of the tension applied.

n directly proportional to √T

3. Laws of Mass:- For a given string and tension applied on the string. Thefrequency of vibration is inversely proportional to the square root of mass / unit length.

n directly proportional to 1/√m

n = 1/2l √T/πr²e

Answer 2

Answer:

Laws of Vibrations in a Stretched String

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STATE AND USE THE LAW OF LENGTH FROM THE LAWS OF TRANSVERSE VIBRATIONS OF A STRING - DEFINITION

Law of length: The fundamental frequency is inversely proportional to the resonating length (L) of the string. So,

f∝

L

1

STATE AND USE THE LAW OF TENSION FROM THE LAWS OF TRANSVERSE VIBRATIONS OF A STRING - DEFINITION

Law of Tension: The fundamental frequency is directly proportional to the square root of the tension. So,

f∝

T

STATE AND USE THE LAW OF MASS FROM THE LAWS OF TRANSVERSE VIBRATIONS OF A STRING - DEFINITION

Law of mass: The fundamental frequency is inversely proportional to the square root of the mass per unit length.

f∝

μ

1

Velocity of a transverse wave travelling in stretched string is given by:

v=

μ

T

where T is the tension in the string and μ is the mass per unit length.

Now, the fundamental frequency of the stretched string is given by:

f=

2l

1

μ

T

l is the resonating length.

From the above expression, there are three laws of transverse vibration of string.

Law of length: The fundamental frequency is directly proportional to the resonating length (L) of the string.

f∝

L

1

Law of Tension: The fundamental frequency is directly proportional to the square root of the tension.

f∝

T

Law of Mass: The fundamental frequency is inversely proportional to the square root of the mass per unit length.

f∝

μ

1

We can verify the three laws of vibration as follows:

Law of length (f ∝ 1/L): When we take different tuning forks of different frequencies, and measure the resonating length for each of them keeping tension applied and the material of the wire as constant. The product of frequency and resonating length of one tuning fork was found equal to the frequency and resonating length of another tuning fork. This verifies the law of length.

Law of tension (f ∝ √T): The resonance of different tuning forks of different frequencies was observed by varying tension keeping resonating length and wire as constant. When a graph for f vs √T is plotted, a straight line is obtained. This verifies the law of tension.

Laws of mass (f ∝ 1/√μ): The resonance is observed by taking different tuning forks of different frequencies and different wires with separate mass per unit length (μ) keeping resonating length and tension applied as constant. When the graph for f vs 1√μ is plotted and the graph is found to be a straight line. So, law of mass is verified.