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Physics 5 Marks Questions

PART - 2 CH - 14 Waves · Gujarat Board (GSEB) STD 11 Science (GSEB - English Medium). 17 questions.

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Question 15 Marks
A progressive harmonic wave on a string is expressed as follow
$
y(x, t)=7.5 \sin (0.0050 x+12 t+\pi / 4)
$
(a) Find the speed at a point $x=1 cm$ on time $t=1$ sec. Is this speed is equal to the speed of wave propagation?
(b) Find the location of those points of the string whose tranverse displacement and speed are the same as that of the point located at $x=1 cm$ at times $t =2 s, 5 s$ and $11s.$
Answer
(a) $y(x, t)=7.5 \sin \left(0.0050 x+12 t+\frac{\pi}{4}\right)$
On comparing the above equation with the following equation of normal progressive wave.
$y=a \sin [k x+\omega t+Q]$
Hence, $k=0.0050$ and $\omega=12$
$\text {Speed of wave}\quad = v =n \lambda=(2 \pi n) \times \frac{\lambda}{2 \pi}=\frac{\omega}{ k }$
$ \begin{array}{l}\text {Speed of wave}\quad\text { (v) }=\frac{12}{0.0050}=\frac{12000}{5}=2400 cm / s \\v=\frac{2400}{100} m / s=24 m / s\end{array}$
In given equation displacement at $x=1 cm, \pm=1 s$
$y(1,1)=7.5 \sin \left(0.005+12+\frac{\pi}{4}\right)$
Put the value in given equation
$\begin{array}{l}=7.5 \sin \left(12.005+\frac{\pi}{4}\right) \\=7.5 \sin \left(12.005+\frac{3.14}{4}\right) \\=7.5 \sin (12.005+0.785)\end{array}$
$\begin{aligned} & =7.5 \sin (12.79) \\ & =7.5 \sin \left(12.79 \times \frac{180}{\pi}\right) \\ & \quad\left[\because \pi \text { Radian }=180^{\circ}\right] \\ & =7.5 \sin \left(732.83^{\circ}\right) \\ & =7.5 \sin \left(720^{\circ}+12.83^{\circ}\right) \\ & =7.5 \sin 12.83^{\circ} \\ \text { or } \quad y(1,1) & =7.5 \times 0.2215 \\ & =1.67 cm \end{aligned}$
Speed of oscillation on point
$\begin{aligned} v & =\frac{d y}{d t} \\ v & =7.5 \times 12 \cos \left(0.0050 x+12 t+\frac{\pi}{4}\right) \\ & =90.0 \cos \left(0.0050 x+12 t+\frac{\pi}{4}\right) \\ x & =1 cm, t=1 \text { second } \\ v & =90 \cos (0.005 \times 1+12 \times 1+0.785) \\ & =90 \cos (12.79) \\ & =90 \cos \left(732.83^{\circ}=90 \cos 12.83^{\circ}\right) \\ & =90 \times 0.9751=87.76 cm / s \end{aligned}$
Hence, speed of osicllation point $ \simeq$ 88 cm/s
But speed of wave =24 m/s
Hence, it is clear that the speed of oscillation of the point is different from the speed of wave motion. Hence not equivalent.
(b) Given equation
$y=7.5 \sin \left(0.0050 x+12 t+\frac{\pi}{4}\right)$
Progressive wave equation
$y=a \sin (\omega t+k x+\phi)$ on compare
$k =0.005$ Radian/cm
$\lambda=\frac{2 \pi}{ k }=\frac{2 \times 3.142}{0.005}=12.57 m$
In a transverse wave the displacement of all points is equal. Which are at distance $\lambda, 2 \lambda, 3 \lambda \ldots$ etc. Therefore displacement of all point $12.57 m, 25.14 m, 37.71 m$ will be same.
Thus, all the points when $n= \pm 1, \pm 2, \pm 3, \pm 4, \ldots x=$ 1 cm at other distance but displacement will be same.
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Question 25 Marks
Define the following :
(i) Frequency (ii) Time period (iii) Amplitude (iv) Wave length (v) Phase angle (vi) Angular frequency (vii) Propagation con (viii) Wave velocity.
Answer
(i) Frequency : The number of vibrations made by a particle in a second is called frequency. Its S.I. unit is Hertz. We can represent it by U.
Image
(ii) Time period : The time raken by a particle for one vibration is called time period. Time period is the reciporcal of frequency. That is, time period
$T =\frac{1}{n}=\frac{2 \pi}{\omega}$
(iii) Amplitude : The maximum displacement from mean position of particle is called amplitude. It is represented by 6a'.
(iv) Wave length : The distance between two nearest particle vibrating in the same phase is called wave length. We represent it by ' $\lambda$ '.
(v) Phase angle : The phase angle of a vibrating particle at any instant reveals the state of motion at that instant. It is represented by $\phi$.
(vi) Angular frequency : The rate of change in the phase angle of the particle with time is called angular frequency. Angular frequency $\omega=2 \pi n=\frac{2 \pi}{T} rad / sec$
(vii) Propogation constant : If the distance between any two vibrating points in the wave is $\lambda$ and phase difference is $2 \pi$. The phase difference between vibrating particles located at unit distance called propagation constant.
(viii) Wave velocity : When there is wave motion the distance the distance covered by the vibrational disturbance in one second is called wave velocity.
Wave velocity $v =\frac{\lambda}{ T }$ or $v = n \lambda$
$\text {or}\quad v=\frac{\omega}{2 \pi} \times \frac{2 \pi}{k}$
$\text {or}\quad v=\frac{\omega}{k} \text { meter } / sec .$
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Question 45 Marks
Calculate the frequency of the original tone in stretched cord. Explain the fundamental and overtones of a string and prove that both even and odd harmonics are produced in the string.
Answer
SELF
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Question 55 Marks
Write a labelled diagram of resonance tube and explain it. With its help establish formulas to determine the velocity of sound.
OR
Make a labelled diagram of resonance tube and describe its structure and establish the formula to find the velocity of sound at room temperature.
Answer
SELF
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Question 65 Marks
Prove that closed argon pipe produced only odd harmonics whereas both odd and even harmonic are produced in an open argon pipe.
Answer
SELF
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Question 105 Marks
What is Beat? Analyze it mathematically and prove that the number of beat per second is equal to the difference of the frequencies of both the sound sources. How can the frquency of a tunning fork be clamed down with the help of pulses?
Answer
SELF
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Question 115 Marks
Explain the experimental demonstration of in- terference by making a labelled diagram of a quinke tube.
Answer
SELF
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Question 125 Marks
What is the principle of superposition? On what factors frequency and amplitude of the resultant wave depend? What effect can be produced by the superposi- tion of two sound waves? Exaplain interference of sound wave and analyze it mathematically.
Answer
SELF
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Question 135 Marks
Explain the velocity of sound in different medium and write the factor affecting the velocity of sound in gas.
Answer
SELF
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Question 145 Marks
What are progressive wave? Establish the equation representing progressive wave and explain phase and path difference.
OR
Establish the equation of plane progressive wave and find out phase difference.
Answer
SELF
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Question 165 Marks
What are electromagnetic waves? Explain the characteristics of waves. Prove that $v=n \lambda$ where $V$ is the velocity $n$ is frequency and $\lambda$ is the wavelength.
Answer
SELF
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Question 175 Marks
What are waves and wave speed? For wave propagation. What are the essential properties? How many types of waves are there? Explain by giving examples.
Answer
SELF
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5 Marks Questions - Physics STD 11 Science Questions - Vidyadip