A hiker shouts toward a vertical cliff 675 m away. The echo is heard 4.00 s later.

(a) What is the speed of sound of the hiker's voice in air? m/s
(b) The wavelength of the sound is 0.774 m. What is its frequency? Hz
(c) What is the period of the wave?

(a) It depends upon the air temperature. Usually about 340 m/s is used for the sound speed.

(b) frequency =
(sound wave speed)/(wavelength)
= 340/0.774
= ___ Hz

(c) Period = 1/(frequency)
(in seconds)

thanks, you were right.

To solve the problem, we need to use the following formulas:

(a) Speed of sound (v) = Distance / Time
(b) Frequency (f) = Speed of sound / Wavelength
(c) Period (T) = 1 / Frequency

(a) First, let's find the speed of sound using the given distance and time:
Speed of sound (v) = Distance / Time
Speed of sound (v) = 675 m / 4.00 s
Speed of sound (v) = 168.75 m/s

(b) Now, we can find the frequency using the speed of sound and wavelength:
Frequency (f) = Speed of sound / Wavelength
Frequency (f) = 168.75 m/s / 0.774 m
Frequency (f) = 218.14 Hz

(c) Finally, we can find the period using the frequency:
Period (T) = 1 / Frequency
Period (T) = 1 / 218.14 Hz
Period (T) = 0.00458 s or 4.58 ms

To solve this problem, we can use the formula for calculating the speed of sound in air:

Speed of sound (v) = Distance (d) / Time (t)

(a) To find the speed of sound, we need to calculate the distance traveled by the sound wave. Since the hiker shouts towards a vertical cliff, the sound wave travels from the hiker to the cliff and back to the hiker (round trip). Therefore, the total distance traveled by the sound wave is twice the distance between the hiker and the cliff.

Given:
Distance (d) = 675 m (twice the distance between the hiker and the cliff)
Time (t) = 4.00 s

Using the formula:
v = d / t
v = 675 m / 4.00 s

Calculating this, we get:
v ≈ 168.75 m/s

So, the speed of sound of the hiker's voice in air is approximately 168.75 m/s.

(b) To find the frequency, we can use the formula for the speed of sound:

v = λ * f

Given:
Speed of sound (v) = 168.75 m/s
Wavelength (λ) = 0.774 m

Rearranging the formula:
f = v / λ
f = 168.75 m/s / 0.774 m

Calculating this, we get:
f ≈ 218.08 Hz

So, the frequency of the sound wave is approximately 218.08 Hz.

(c) The period of a wave is the inverse of its frequency. Therefore, we can calculate the period using the formula:

Period (T) = 1 / frequency (f)

Given:
Frequency (f) = 218.08 Hz

Using the formula:
T = 1 / f
T = 1 / 218.08 Hz

Calculating this, we get:
T ≈ 0.0046 s

So, the period of the sound wave is approximately 0.0046 s.