This article shows how you can make a 555 timer sound generator. This generator produces square wave and allows amplitude control.

Step 1: Design the Circuit

I drawn the circuit with PSpice software:

The three Q4 transistors are acting as an equivalent resistor thus reducing the amplitude of output signal. A higher Q4 transistor base current reduces the output voltage and thus AC signal magnitude.

Calculate minimum equivalent resistance at input of Q1 transistor:

Req = Vb1/Ib1

Ib1 = Ie1 / (Beta + 1)

 = Ie2 / (Beta + 1) / (Beta + 1)

 = Ie3 / (Beta + 1) / (Beta + 1) / (Beta + 1)

Ie3 = (Vs - Vbe*4) / Rb4

= 0.01589743589 A

Ib1 = 0.0000017166 A

Req = 5.2429 Megohms

Calculate high pass filter frequency:

fh = 1/(2*pi*(Rs1+Rs2+Rspeaker)*Cs2)

 = 1/(2*pi*(22*2 ohms + 4 ohms)*(220*10^-6))

= 15.0714908231 Hz

Calculate the time constants of charging C1 or C2 capacitor:

Tmin = 1/(Rc1a*C1) = 0.22 seconds

Tmax = 1/((Rc1a+Rc1b)*C1) = 22.22 seconds

Calculate the 555 Timer minimum and maximum frequency:

fmin = 1/(1.386*(Rd2 + Rf)*Cd) = 35.8955582836 Hz

fmax = 1/(1.386*Rd*Cd) = 7215.00721501 Hz or 7.215 kHz

(555 Timer Information: https://www.electronics-tutorials.ws/waveforms/555_oscillator.html)

Step 2: Simulations

Simulations show a reasonable high amplitude oscillation because I assumed a speaker impedance of 100 ohms. in real life the speaker impedance could be as low as 4 ohms and thus reducing the output amplitude.