Answer: the observer needs to move toward the train at 82.3 km/hr to hear a pitch of 750 Hz.
Step-by-step explanation:
We can use the formula for the Doppler effect to solve this problem. The Doppler effect describes the change in frequency of a wave (such as sound) due to the relative motion of the source and observer. The formula for the Doppler effect in this case is:
f' = f (v + u) / (v + u')
where:
f is the frequency of the sound emitted by the train (800 Hz)
f' is the frequency of the sound heard by the observer (750 Hz)
v is the speed of sound (343 m/s)
u is the speed of the train (120.0 km/hr)
u' is the speed of the observer relative to the train (what we want to find)
We need to convert the speeds to the same units (m/s) to use the formula. We have:
u = 120.0 km/hr = (120.0 km/hr) * (1000 m/km) / (3600 s/hr) = 33.33 m/s
v = 343 m/s
f = 800 Hz
f' = 750 Hz
Now we can solve for u':
f' = f (v + u) / (v + u')
750 Hz = 800 Hz (343 m/s + 33.33 m/s) / (343 m/s + u')
750 Hz (343 m/s + u') = 800 Hz (343 m/s + 33.33 m/s)
257250 Hz + 750 u' = 274400 Hz
750 u' = 17150 Hz
u' = 22.86 m/s
Finally, we convert u' to km/hr:
u' = 22.86 m/s * (3600 s/hr) / (1000 m/km) = 82.3 km/hr
Therefore, the observer needs to move toward the train at 82.3 km/hr to hear a pitch of 750 Hz.