Length of a sonometer wire between two fixed ends is 110 cm. If the fundamental frequencies are

Name: Problem 57, Chapter 10: Objective Physics : NEET 2020 Examination textbook Gurukul Oswal
Uploaded: 2021-10-21T04:48:06-08:00
Duration: 1 min 8 s
Channel: Kumari Shilpi
Description: Length of a sonometer wire between two fixed ends is 110 cm. If the fundamental frequencies are in the ratio of 1: 2: 3, then what is the ratio of lengths of these segments of the wire? (a) 3: 2: 1 (b) 6: 3: 2 (c) 6: 2: 3 (d) 2: 3: 6

step 1 I have a question in this there is a length of sonometer wire which is 110 centimeters okay and

Question

Length of a sonometer wire between two fixed ends is $110 \mathrm{~cm}$. If the fundamental frequencies are in the ratio of $1: 2: 3$, then what is the ratio of lengths of these segments of the wire? (a) $3: 2: 1$ (b) $6: 3: 2$ (c) $6: 2: 3$ (d) $2: 3: 6$

   Length of a sonometer wire between two fixed ends is $110 \mathrm{~cm}$. If the fundamental frequencies are in the ratio of $1: 2: 3$, then what is the ratio of lengths of these segments of the wire?
(a) $3: 2: 1$
(b) $6: 3: 2$
(c) $6: 2: 3$
(d) $2: 3: 6$

Objective Physics : NEET 2020 Examination textbook Gurukul Oswal

Gurukul Oswal… 2020 Edition

Chapter 10, Problem 57

Instant Answer

Solved by Expert Kumari Shilpi

10/21/2021

Step 1

We also know that frequency is inversely proportional to length. Therefore, the ratio of lengths of these segments of the wire will be the inverse of the given ratio of frequencies. Show more…

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Length of a sonometer wire between two fixed ends is $110 \mathrm{~cm}$. If the fundamental frequencies are in the ratio of $1: 2: 3$, then what is the ratio of lengths of these segments of the wire? (a) $3: 2: 1$ (b) $6: 3: 2$ (c) $6: 2: 3$ (d) $2: 3: 6$

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Key Concepts

Fundamental Frequency of a Vibrating String

The lowest or fundamental frequency at which a string vibrates is determined by its length, tension, and mass per unit length. Specifically, for a string fixed at both ends, the fundamental frequency is given by the formula f = (1/2L)?(T/?), where L is the length of the string. This concept is essential in understanding how vibrations and sound production occur in strings.

Inverse Relationship Between Frequency and String Length

For a string with constant tension and linear density, the fundamental frequency is inversely proportional to the length of the string. This means that shorter segments of the string will vibrate at higher frequencies, while longer segments will produce lower frequencies. This principle allows one to deduce the ratios of lengths when the ratios of corresponding fundamental frequencies are provided.

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