23. (1 pt)
the signal reached an instantaneous phase of 90 ̊?
If 100 Hz pure tone with a starting phase of 0 ̊ is listened to for 1.5 s, then how many times has
a) 50
b) 100
c) 150
d) 200
e) 250
100 Hz = 100 cycles/s.
100c./s. * 1.5s. = 150 Cycles.
To solve this problem, we need to understand the concept of phase and frequency.
Phase: A phase represents the position of a waveform within its cycle. It is usually measured in degrees (°). A phase of 0° means the waveform is at the starting point of its cycle, while a phase of 90° means the waveform has completed one-fourth of its cycle.
Frequency: Frequency refers to the number of cycles of a waveform that occur in one second. It is measured in Hertz (Hz). For example, a frequency of 100 Hz means the waveform completes 100 cycles in one second.
Now, let's calculate the number of times the signal reaches an instantaneous phase of 90° for a 100 Hz tone listened to for 1.5 seconds.
Frequency = 100 Hz
Time = 1.5 seconds
To calculate the number of cycles, we multiply the frequency by the time:
Number of cycles = Frequency x Time
a) For a frequency of 50, we have:
Number of cycles = 50 Hz * 1.5 s = 75 cycles
b) For a frequency of 100, we have:
Number of cycles = 100 Hz * 1.5 s = 150 cycles
c) For a frequency of 150, we have:
Number of cycles = 150 Hz * 1.5 s = 225 cycles
d) For a frequency of 200, we have:
Number of cycles = 200 Hz * 1.5 s = 300 cycles
e) For a frequency of 250, we have:
Number of cycles = 250 Hz * 1.5 s = 375 cycles
Thus, the number of times the signal reaches an instantaneous phase of 90° for different frequencies over 1.5 seconds are:
a) 75 times
b) 150 times
c) 225 times
d) 300 times
e) 375 times