Learn to Create a Robotic Device Using Arduino in the Free Webinar. Register Now
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-1023-196
+91-120-4616500
CART 0
Use Coupon: CART20 and get 20% off on all online Study Material
Welcome User
OR
LOGIN
Complete Your Registration (Step 2 of 2 )
Free webinar on Robotics (Block Chain) Learn to create a Robotic Device Using Arduino
30th Jan @ 5:00PM for Grade 1 to 10
Two waves, each having a frequency of 100 Hz and a wavelength of 2.0 cm, are travelling in the same direction on a string. What is the phase difference between the waves (a) if the second wave was produced 0.015 s later than the first one at the same place, (b) if the two waves were produced at the same instant but the first one was produced a distance 4.0 cm behind the second one ? (c) If each of the waves has an amplitude of 2.0 mm, what would be the amplitudes of the resultant waves in part (a) and (b)? Two waves, each having a frequency of 100 Hz and a wavelength of 2.0 cm, are travelling in the same direction on a string. What is the phase difference between the waves(a) if the second wave was produced 0.015 s later than the first one at the same place,(b) if the two waves were produced at the same instant but the first one was produced a distance 4.0cm behind the second one ?(c) If each of the waves has an amplitude of 2.0 mm, what would be the amplitudes of the resultantwaves in part (a) and (b)?
f = 100 Hz, λ = 2 cm = 2 * 10 base 2 m ∴ wave speed, v = f λ = 2 m/s a) in 0.015 sec 1^ST wave has travelled x = 0.015 * 2 = 0.03 m = path diffn ∴ corresponding phase difference, ∅ = 2π*/λ = {2π/ (2 * 10^2)} * 0.03 = 3π. b) Path different x = 4 cm = 0.04 m ⇒ ∅ = (π/λ)x = {(2π/2 * 10^2) * 0.04} = 4 π. C) The waves have same frequency, same wavelength and same amplitude Let, Y base 1 = r sin wt y base 2 = r sin (wt + ∅) ⇒ Y = Y base 1 + y base 2 = [r sin wt + (wt + ∅) = 2r sin (wt + ∅/2) cos (∅/2) ∴ resultant amplitude = 2r cos ∅/2 So when ∅ = 3π, r = 2 * 10^ 3 m R base res = 2 * (2 * 10^3) cos (3π/2) = 0 Again, when ∅/2π, R base res = 2 * (2 * 10^3) cos (4π/2) = 4mm.
Post Question
Dear , Preparing for entrance exams? Register yourself for the free demo class from askiitians.
points won -