If the highest frequency a song is 10 kHz and it is encoded at 16 bits per sample what is the minimum number of bytes needed to encode the 3 minute song?

The key to this question is to remember the Nyquist rate of a signal. This is the lowest sample rate which can be used for a signal without losing valid frequencies or gaining incorrect frequencies. This is equal to twice the highest frequency.

Therefore the sample rate needs to be 20 kHz. Since there are 16 bits per sample the number of bits per second is 16 multiplied by 20 000 which is 320 000 bits per second.

To calculate the number of bits in 3 minutes we need to multiply 320 000 by the number of seconds in 3 minutes. Which gives:
320 000 x 3 x 60 = 57 600 000 bits 

Remember to divide by 8 to get it in bytes, since there are 8 bits in a byte. This finally gives:
57 600 000/8 = 7 200 000 bytes = 7.2 Megabytes

DM
Answered by David M. Physics tutor

6069 Views

See similar Physics A Level tutors

Related Physics A Level answers

All answers ▸

A ball of mass 0.25 kg is travelling with a velocity of 1.2 m/s when it collides with an identical, stationary ball. After the collision, the two balls move together with the same velocity. How fast are they moving?


What is the angular velocity of a car wheel which diameter is d = 15 mm if the car velocity is of 120 km/h?


A spacecraft needs to be slowed down from a speed of 96m/s to 8.2m/s. This can be done by firing an object as the spacecraft is moving. If the mass of the spacecraft is 6730kg and the object is 50kg, calculate the velocity of the ejected object.


A cable with a diameter of 6mm is used to lift crate. Calculate the mass of the crate required to create a stress of 350 MPa.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences