Question

You and your surfing buddy are waiting to catch a wave a few hundred meters off the beach. The waves are conveniently sinusoidal, and you notice that when you're on the top of one wave and moving toward your friend, she is exactly halfway between you and the trough of the wave. 1.50 seconds later, your friend is at the top of the wave. You estimate the horizontal distance between you and your friend at 8.00 m. (a) What is the frequency of the waves?

Answer 1

(a) The frequency of the waves is ¹/₆ Hz ≈ 0.167 Hz

(b) The speed of the waves is 5¹/₃ m/s ≈ 5.33 m/s

$\texttt{ }$

Further explanation

Let's recall the speed of wave and intensity of wave formula as follows:

$\large {\boxed {v = \lambda f}}$

f = frequency of wave ( Hz )

v = speed of wave ( m/s )

λ = wavelength ( m )

$\texttt{ }$

$\large {\boxed {I = 2 \pi^2 A^2 f^2 \rho v}}$

I = intensity of wave ( W/m² )

A = amplitude of wave ( m )

f = frequeny of wave ( Hz )

ρ = density of medium ( kg/m³ )

v = speed of wave ( m/s )

Let's tackle the problem!

$\texttt{ }$

Given:

time taken = t = 1.50 seconds

distance covered = d = 8.00 m

Asked:

(a) frequency of the waves = ?

(b) speed of the waves = ?

Solution:

Question (a):

$t = \frac{1}{4}T$

$1.50 = \frac{1}{4}T$

$T = 4 \times 1.50$

$T = 6 \texttt{ seconds}$

$\texttt{ }$

$f = \frac{1}{T}$

$f = \frac{1}{6} \texttt{ Hz}$

$\texttt{ }$

Question (b):

$d = \frac{1}{4}\lambda$

$8.00 = \frac{1}{4}\lambda$

$\lambda = 8.00 \times 4$

$\lambda = 32 \texttt{ m}$

$\texttt{ }$

$v = \lambda f$

$v = 32 \times \frac{1}{6}$

$v = 5\frac{1}{3} \texttt{ m/s}$

$\texttt{ }$

Learn more

• Doppler Effect : brainly.com/question/3841958
• Example of Doppler Effect : brainly.com/question/810552
• Sound Waves Cannot Travel In Space. : brainly.com/question/546436
• Frequency of The Beats - Doppler Effect : brainly.com/question/12367463

$\texttt{ }$

Answer details

Grade: College

Subject: Physics

Chapter: Sound Waves

Answer 2

Answer:

(a): The frequency of the waves is f= 0.16 Hz

Explanation:

T/4= 1.5 s

T= 6 sec

f= 1/T

f= 0.16 Hz (a)