Final answer:
To increase the loudness of a musical note modeled by a sine function, the amplitude of the wave should be increased. For the note E represented by the function y = asin(1320πx), setting a to a higher value, such as 2, results in a louder sound. Additionally, using the formula speed = frequency × wavelength, one can calculate the speed of the musical note "A" with given frequency and wavelength.
Step-by-step explanation:
To make the musical note E louder than the original when modeled by the function y = asin(1320πx), where a = 1 and x is the time in seconds, you would need to increase the amplitude a of the wave. The amplitude correlates with the loudness of the sound; by increasing the amplitude, you increase the sound's intensity and hence its loudness. For example, if you set a to 2, the new function will become y = 2sin(1320πx), resulting in a sound wave with twice the amplitude, which would be perceived as louder.
Looking at the given information for the musical note "A", which has a frequency of 440 Hz and a wavelength of 0.784 m, you can calculate the speed of the sound wave by using the formula speed = frequency × wavelength. So the speed of the musical note "A" would be 440 Hz × 0.784 m = 344.96 m/s.
The wave function y (x, t) = A sin (kx — wt) describes a sinusoidal wave, where A represents the amplitude, k the wave number, and w the angular frequency. Since the amplitude can be read directly from the equation, to increase the loudness, you would adjust A to a higher value.