The tip of each prong of a tuning fork emitting a note of 320Hz vibrates in SHM with an amplitude of 0.50mm. What is the speed of each tip when its displacement is zero?

As with any question that lists numbers, the first thing to do is to note down the known variables:

f = 320 Hz

A = 0.50 mm

x = 0 mm

v = ?

This requires use of two of the simple harmonic motion (SHM) equations: x = Asinwt and v = Awcoswt. The second equation is simply the derivative of the first equation. Firstly, substitute the known values into the first equation to find t:

x = Asinwt

0 = 0.50 * sinwt

w = 2pif  (definition of angular frequency)

0 = 0.50 * sin(2pi320)t

This gives (2pi320)t = k*pi, where k is a whole number. This is because sine of any multiple of pi will give zero, which can be seen from the graph of sine. 

This gives t = k / 2*320 = k / 640.

Substitute this value of t into the equation for v to find the speed:

v = Awcoswt

   = 0.50 * (2pi320) * cos((2pi320)*(k/640))

   = pi * 320 * cos(k*pi)

The cosine of any multiple of pi is either +1 or -1. Since we only need the speed of the tip, whether it is + or - doesn't matter. Therefore:

v = pi * 320 * 1

   = 320pi mm/s

Answered by Ellie S. Physics tutor

13980 Views

See similar Physics A Level tutors

Related Physics A Level answers

All answers ▸

What does the photoelectric effect demonstrate?


Can you talk me through how to solve problems on projectiles? I always get confused


A person stands on top of a cliff and throws a ball with a speed of 20 m/s at an angle of 10 degrees from above the horizontal into the sea. What is the height of the cliff to 1 decimal place?


Name an experiment proving that light is wave and one that is proving that light consists of particles.


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2024

Terms & Conditions|Privacy Policy