A hiker shouts toward a vertical cliff 660 m away. The echo is heard 4.00 s later.

(a) What is the speed of sound of the hiker's voice in air?
(b) The wavelength of the sound is 0.758 m. What is its frequency?
(c) What is the period of the wave?

To find the answers to these questions, we can use the speed equation:

Speed = Distance / Time

a) To find the speed of sound, we need to calculate the distance it traveled in the given time. The sound traveled from the hiker to the cliff and then back, covering a total distance of twice the given distance (2 * 660 m = 1320 m). The time for this round trip is 4.00 s. Therefore, we can calculate the speed:

Speed = Distance / Time
Speed = 1320 m / 4.00 s
Speed ≈ 330 m/s

So, the speed of sound in air is approximately 330 m/s.

b) The wavelength (λ) of the sound wave is given as 0.758 m. To find the frequency (f), we can use the equation:

Speed = Wavelength * Frequency

From part (a), we know the speed is 330 m/s and the wavelength is 0.758 m. Now we can solve for frequency:

330 m/s = 0.758 m * Frequency
Frequency ≈ 434 Hz

Therefore, the frequency of the sound wave is approximately 434 Hz.

c) The period (T) of a wave is the inverse of its frequency. We can find the period by using the equation:

T = 1 / f

From part (b), we know the frequency is 434 Hz. Substituting this value into the equation, we can find the period:

T = 1 / 434 Hz
T ≈ 0.0023 s

Thus, the period of the wave is approximately 0.0023 s.