(i) For the wave on a string described in Exercise 15.11, do all the points on the string oscillate with the same (a) frequency, (b) phase, (c) amplitude? Explain your answers. (ii) What is the amplitude of a point 0.375 m away from one end?
Solution and Explanation
(i) Yes, except at the nodes
Yes, except at the nodes
No, 0.042 m
Explanation:
(i) All the points on the string oscillate with the same frequency, except at the nodes which have zero frequency.
All the points in any vibrating loop have the same phase, except at the nodes.
All the points in any vibrating loop have different amplitudes of vibration.
The given equation is:
y(x,t)=0.06 sin \((\frac{2\pi}{3}x)\) cos (120 πt)
For x = 0.375 m and t = 0
Amplitude= Displacement= 0.06 sin \((\frac{2\pi}{3}x)\) cos 0
= 0.06 sin \((\frac{2\pi}{3}× 0,375)×1\)
= 0.06 sin (0.25 π)=0.06 sin \((\frac{\pi}{4})\)
= 0.06× \(\frac{1}{\sqrt2}=0.042\, m\)
Top Questions on Waves
- Displacement of a wave is expressed as $$ x(t) = 5 \cos \left( 628t + \frac{\pi}{2} \right) \, \text{m}. $$ The wavelength of the wave when its velocity is 300 m/s is:
- The equation of a wave travelling on a string is $ y = \sin[20\pi x + 10\pi t] $, where x and t are distance and time in SI units. The minimum distance between two points having the same oscillating speed is :
- The amplitude and phase of the wave when two travelling waves given as $ y_1(x, t) = 4 \sin(\omega t - kx) $ and $ y_2(x, t) = 2 \sin\left(\omega t - kx + \frac{2\pi}{3}\right) $ are superimposed.
- A light wave is propagating with plane wave fronts of the type \( x + y + z = \text{constant} \). The angle made by the direction of wave propagation with the \( x \)-axis is:
Two plane polarized light waves combine at a certain point, whose "E" components are: \[ E_1 = E_0 \sin \omega t, \quad E_2 = E_0 \sin \left( \omega t + \frac{\pi}{3} \right) \] Find the amplitude of the resultant wave.
Questions Asked in CBSE Class XI exam
- Briefly comment on "The purpose of the author’s journey to Mount Kailash."
- CBSE Class XI
- Silk road
- Mention the three phases of the author’s relationship with his grandmother before he left the country to study abroad.
- CBSE Class XI
- The Portrait of a lady
- What do you understand by isoelectronic species? Name a species that will be isoelectronic with each of the following atoms or ions.
- F-
- Ar
- Mg2+
- Rb+
- CBSE Class XI
- Electronic Configurations Of Elements And The Periodic Table
- Bromine monochloride, BrCl decomposes into bromine and chlorine and reaches the equilibrium:
\(2BrCl (g) ⇋ Br_2 (g) + Cl_2 (g)\)
for which Kc = 32 at 500 K. If initially pure BrCl is present at a concentration of 3.3 × 10–3 mol L–1, what is its molar concentration in the mixture at equilibrium?- CBSE Class XI
- Law Of Chemical Equilibrium And Equilibrium Constant
Give reasons for the following.
(i) King Tut’s body has been subjected to repeated scrutiny.
(ii) Howard Carter’s investigation was resented.
(iii) Carter had to chisel away the solidified resins to raise the king’s remains.
(iv) Tut’s body was buried along with gilded treasures.
(v) The boy king changed his name from Tutankhaten to Tutankhamun.- CBSE Class XI
- Discovering Tut: The saga Continues