HSC Science (General) 12th Standard Board Exam - Maharashtra State Board Important Questions

A pipe open at both ends resonates to a frequency ‘n₁’ and a pipe closed at one end resonates to a frequency ‘n₂’. If they are joined to form a pipe closed at one end, then the fundamental frequency will be ______.

(A)  `(n_1n_2)/(2n_2+n_1)`

(B) `(2n_2n_1)/(2n_2+n_1)`

(C) `(2n_2n_1)/(n_1+n_2)`

(D) `(n_2+2n_1)/(n_1n_2)` 

Two sound notes have wavelengths 83/170 m and 83/172 m in the air. These notes when sounded together produce 8 beats per second. Calculate the velocity of sound in the air and frequencies of the two notes.

State the cause of end correction.

Find the end correction for the pipe open at both the ends in fundamental mode.

What should be tension applied to a wire of length 1 m and mass 10 gram, if it has to vibrate with fundamental frequency of 50 Hz?

A sonometer wire vibrates with three nodes and two antinodes, the corresponding mode of vibration is ...................

a) First overtone

b) Second overtone

c) Third overtane

d) Fourth overtone

A tube open at both ends has length 47 em. Calculate the fundamental frequency of air column. (Neglect end correction. Speed of sound in air is 3.3 x 10²m/s}

Draw neat labelled diagrams for modes of vibration of an air column in a pipe when it is closed at one end.

Hence derive an expression for fundamental frequency in each case.

In Melde’s experiment, the number of loops on a string changes from 7 to 5 by the addition of 0.015 kgwt. Find the initial tension applied to the string.

A stretched wire emits a fundamental note of frequency 256 Hz. Keeping the stretching force constant and reducing the length of wire by 10 cm, the frequency becomes 320 Hz. Calculate the original length of wire.

Show the formation of stationary waves diagramatically

In the stationary wave, the distance between a node and its adjacent antinode is _______.

(a) λ

(b) `lambda/4`

(c) `lambda/2`

(d)  2λ

In Melde’s experiment, when the tension in the string is 10 g wt then three loops are obtained. Determine the tension in the string required to obtain four loops, if all other conditions are constant.

What is meant by harmonics?

Show that only odd harmonics are present as overtones in the case of an air column vibrating in a pipe closed at one end.

Assuming expression for impedance in a parallel resonant circuit, state the conditions for parallel resonance. Define resonant frequency and obtain an expression for it.

Show that even as well as odd harmonics are present as overtones in the case of an air column vibrating in a pipe open at both the ends.

A wheel of moment of inertia 1 kg.m² is rotating at a speed of 30 rad/s. Due to friction on the axis, it comes to rest in 10 minutes. Calculate the average torque of the friction.

A stretched sonometer wire is in unison with a tuning fork. When the length of the wire is increased by 5%, the number of beats heard per second is 10. Find the frequency of the tuning fork.

A sonometer wire 1 metre long weighing 2 g is in resonance with a tuning fork of frequency 300 Hz. Find tension in the sonometer wire.