SATHEE: Waves - Result Question 43

Waves - Result Question 43

45. A string is stretched between two fixed points separated by $75.0 c m$ . It is observed to have resonant frequencies of $420 H z$ and $315 H z$ . There are no other resonant frequencies between these two. The lowest resonant frequency for this string is :

(a) $205 H z$

(b) $10.5 H z$

(d) $155 H z$

[2015 RS]

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Answer:

Correct Answer: 45. (c)

Solution:

$f_{n} = \frac{n ν}{2 L}$ where, $n = 1, 2, 3 \dots$ .

The difference between two consecutive resonant frequency is,

$A_{f n} = f_{n + 1} - f_{n} \Rightarrow \frac{(n + 1) v}{2 L} - \frac{n v}{2 L} = \frac{v}{2 L}$

which is also the lowest resonant frequency ( $n = 1$ ).

Thus, for the given string the lowest resonant frequency will be

$= 420 H z - 315 H z$

$= 105 H z$

The difference between any two successive frequencies will be ’ $n$ '

According to question, $n = 420 - 315 = 105 H z$ So the lowest frequency of the string is $105 H z$ .

In a stretched string all multiples of frequencies can be obtained i.e., if fundamental frequency is $n$ then higher frequencies will be $2 n, 3 n, 4 n$ …

Waves - Result Question 43

45. A string is stretched between two fixed points separated by $75.0 c m$ . It is observed to have resonant frequencies of $420 H z$ and $315 H z$ . There are no other resonant frequencies between these two. The lowest resonant frequency for this string is :

Answer:

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Waves - Result Question 43

45. A string is stretched between two fixed points separated by 75.0cm. It is observed to have resonant frequencies of 420Hz and 315Hz. There are no other resonant frequencies between these two. The lowest resonant frequency for this string is :

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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45. A string is stretched between two fixed points separated by $75.0 c m$ . It is observed to have resonant frequencies of $420 H z$ and $315 H z$ . There are no other resonant frequencies between these two. The lowest resonant frequency for this string is :